Reynald Lercier

F. Chabaud and R. Lercier. ZEN, a new toolbox for computing in finite extension of finite rings. User's manual. 1996. Sourceforge project.

Many computational problems need arithmetic operations in polynomial finite rings of Z/nZ where n is an integer (n>1). Integer factorizations, primality testing are for instance such applications. To solve them, programmers use general symbolic mathematical softwares or write specific programs (most of the time in C).

On the first hand, symbolic mathematical softwares (Maple, Mathematica,...) handle with difficulty computations in finite fields. In the worst cases, such programs perform computations with rationals before finally reducing the objects modulo the characteristic n, in the best cases, such reductions are performs but extensions of a finite ring cannot be implemented. In any cases, applications written with such softwares are ten to hundred times slower than an “ad hoc” implementation in C. On the other hand, optimized C libraries deal only with one side of finite fields, mainly Z/nZ.

We hardly believe we can keep the efficiency of these C libraries while working in any polynomial extension of Z/nZ. We designed the ZEN library to perform efficient arithmetic operations in these sets.

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